If I directly connect two terminals of 3V battery (negative to positive) using copper wire, would it lose all its charge faster compared to another 3V battery that is used to lighten a 1.5V bulb?

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That 1.5 V bulb is not going to survive - it'll burn out. – MSalters Jan 26 '12 at 10:11

The battery has in both cases the same energy content, so it just depends on which method uses more energy per time. This power depends on the resistance $R$ you use to connect both terminals, with a given voltage $U$ derived from Ohm's law: $$P = U^2 /R$$ So, the smaller the resistance, the faster your battery will lose it's stored energy. The copper wire will most likely have a much smaller resistance than the 1.5V light bulb and will discharge your battery in a very short time.
For a precise estimate you also need to know the internal resistance $R_{int}$ of the battery, but that does not change the general picture: $$R = R_{int} + R_{bulb/wire}$$